mlsanityData to 7 Oct 2026

An Information-Theoretic Criterion for Efficient Data Synthesis

arXiv 2605.16379 ↗First posted 11 May 2026cs.LG cs.AI cs.ITcited by 0

On the map: Synthetic data and self-improvement for LLMs → LLM synthetic data generation

Abstract (arXiv)

Synthetic data becomes crucial for large language model training, but its effectiveness is highly inconsistent. We provide an information-theoretic account of this inconsistency: synthetic data improves a model only when the generation-training loop is information-open, i.e., shaped by external signals (verifiers, environments, or rubrics) that inject task-relevant information beyond the model's current distribution. When the loop is information-closed (relying on the model's own outputs without such signals), the data processing inequality ensures that task-relevant information can only decrease, making collapse a predicted outcome. Among information-open pipelines, both efficiency and generalization hinge on the meta-level of supervision: a coarser signal such as binary correctness treats all acceptable outputs as equivalent, so the behavior it teaches is not tied to any particular domain or surface form and generalizes naturally across tasks and domains. These observations lead to a guiding thesis: learning preferentially converges to the most information-efficient signal component available, which accelerates learning when that component is the intended one, but causes reward hacking when a spurious pattern happens to be simpler.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Placed in LLM synthetic data generation, one of 13 directions in Synthetic data and self-improvement for LLMs. Builds on 23 of its 34 references that are in the map. First posted on arXiv 11 May 2026.

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23 of 34 references.

References · 23

  1. 2015Distilling the Knowledge in a Neural Networkcited by 10,076
  2. 2020Scaling Laws for Neural Language Modelscited by 6,411
  3. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,146
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  12. 2023Self-Consuming Generative Models Go MADcited by 239
11 more
  1. 2025KernelBench: Can LLMs Write Efficient GPU Kernels?cited by 206
  2. 2024Is Model Collapse Inevitable? Breaking the Curse of Recursion by Accumulating Real and Synthetic Datacited by 143
  3. 2024A Tale of Tails: Model Collapse as a Change of Scaling Lawscited by 127
  4. 2025Seed-Prover: Deep and Broad Reasoning for Automated Theorem Provingcited by 96
  5. 2025Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2cited by 95
  6. 2025Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experiencecited by 36
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  11. 2025Discovering Expert-Level Nash Equilibrium Algorithms with Large Language Modelscited by 1

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  1. 2026Learning from Synthetic Data without Model Collapse in Iterative Instruction Tuning
  2. 2024Towards a Theoretical Understanding of Synthetic Data in LLM Post-Training: A Reverse-Bottleneck Perspective
  3. 2024Surveying the Effects of Quality, Diversity, and Complexity in Synthetic Data From Large Language Models
  4. 2026Preventing Model Collapse: A Fisher-Rao Perspective on the Dynamics of Training with Synthetic Data
  5. 2026Not All Synthetic Data Is Yours to Learn From
  6. 2025Characterizing Model Behavior Under Synthetic Data Training: An Empirical Study Across Scales and Mixing Ratios
  7. 2025A Theoretical Perspective: How to Prevent Model Collapse in Self-consuming Training Loops
  8. 2025Does Training on Synthetic Data Make Models Less Robust?